I am not sure anyone here can conclusively determine which engine you had. IF the base set was a 5620T then it is 99.9% likely the engine was a 283. IF the base set was a 20320 then the odds are something like 80% 283, 20% 21084. I do not know the relative scarcity of the 21084 so that ratio is an estimate.
If the resolution of the original print is better than the posted scan try looking at the first two 1965 prints with a magnifying glass. On those the cab with the number is visible. to me it looks like it is 3 digits long but it is really hard to tell.
There is one other confusing item. The catalog list price of both the above sets was $34.95, but your parents notes say they paid $37.95. The difference is more than the sales tax. Was the store west of the Mississippi? If so that could account for the difference. In any event that was an expensive gift back then.
MTN, thanks for posting the auction photos.
